GCE Physics B: Physics in Context Additional Sample Questions (Specification B) PHYB4 Physics Inside and Out

Μέγεθος: px
Εμφάνιση ξεκινά από τη σελίδα:

Download "GCE Physics B: Physics in Context Additional Sample Questions (Specification B) PHYB4 Physics Inside and Out"

Transcript

1 hij Teacher Resource Bank GCE Physics B: Physics in Context Additional Sample Questions (Specification B) PHYB4 Physics Inside and Out The Assessment and Qualifications Alliance (AQA) is a company limited by guarantee registered in England and Wales (company number ) and a registered charity (registered charity number ). Registered address: AQA, Devas Street, Manchester M15 6EX. Dr Michael Cresswell, Director General.

2 ADDITIONAL SAMPLE QUESTIONS This document provides a directory of past questions from the legacy AQA GCE Physics Specification B; these questions may prove relevant/useful to both the teaching of the new AQA GCE Physics B: Physics in Context specification and the preparation of candidates for examined units. It is advisable when using these questions that teachers consider how these questions could relate to the new specification. Teachers should be aware of the different treatment of the Quality of Written Communication between the specifications. For specific examples of the style and flavour of the questions which may appear in the operational exams, teachers should also refer to the Specimen Assessment Materials which accompany the specification. A mark scheme has been produced which accompanies this document. 2

3 1. (a) A rocket takes off from the Earth. Exhaust gases are discharged vertically downwards causing the rocket to accelerate vertically upwards. Figure 1 is a sketch graph of the velocity of the rocket against time after lift off. velocity Figure 1 time (i) Describe the acceleration of the rocket during the time shown in Figure 1. (1) (ii) By referring to the graph in Figure 1, explain your answer to part (a)(i). (1) (iii) Suggest why the rocket accelerates as you have described. (1) (b) A satellite has a mass of kg. Initially, it is placed in an orbit of radius m around the Earth. (i) Show that the centripetal force provided by gravitational attraction is N. universal gravitational constant, G = N m 2 kg 2 mass of the Earth = kg 3

4 (ii) Figure 2 shows the variation of the gravitational force F on the satellite with orbital radius R. F/10 4 N R/10 m Figure 2 Show that the data given in Figure 2 are consistent with the inverse square law for the variation of force with distance. (3) (iii) Use data from Figure 2 to find the change in potential energy which occurs when the satellite is raised from its orbit of radius m to an orbit of radius m. (3) 4

5 (iv) When the radius of the orbit is m, the centripetal force on the satellite is N. Calculate the speed of the satellite. (v) State and explain whether energy transformed from chemical energy as the fuel burns is equal to the change in potential energy which occurs when the radius of the orbit is increased. (3) (Total 16 marks) 2. g is the strength of the gravitational field at the surface of the Earth; R is the radius of the Earth. The potential energy lost by a satellite of mass m falling to the Earth s surface from a height R above the surface is A B C D 4mgR 2mgR mgr 2 mgr 4 (Total 1 mark) 5

6 3. (a) Define gravitational field strength at a point in a gravitational field (1) (b) Tides vary in height with the relative positions of the Earth, the Sun and the moon which change as the Earth and the Moon move in their orbits. Two possible configurations are shown in Figure 1. Earth P Moon Sun not to scale Configuration A Moon Sun Earth P not to scale Configuration B Figure 1 Consider a 1 kg mass of sea water at position P. This mass experiences forces F E, F M and F S due to its position in the gravitational fields of the Earth, the Moon and the Sun respectively. (i) Draw labelled arrows on both diagrams in Figure I to indicate the three forces experienced by the mass of sea water at P. (3) 6

7 (ii) State and explain which configuration, A or B, of the Sun, the Moon and the Earth will produce the higher tide at position P. (c) Calculate the magnitude of the gravitational force experienced by 1 kg of sea water on the Earth s surface at P, due to the Sun s gravitational field. radius of the Earth s orbit mass of the Sun = m = kg universal gravitational constant, G = Nm 2 kg 2 (3) (Total 9 marks) 4. A lunar landing module and its parent craft are orbiting the Moon at a height above the surface of m. The mass of the lunar module is kg. The graph below shows the variation of the gravitational force on the module with height above the surface of the Moon. force/10 3 N height above surface/10 m 7

8 (a) (i) Using data from the graph, find the gravitational force on the lunar module and hence find its speed when its orbital height is 6.0 l0 5 m. (3) (ii) Using data from the graph, find the change in gravitational potential energy of the lunar module as it descends from its orbit to the surface of the Moon. (3) (b) The descent of the lunar module is controlled by a set of rockets. Describe how you would use the data which you have already calculated to determine the minimum fuel load which would enable the lunar module to land on the surface of the Moon and subsequently to rejoin its parent craft in orbit. State what additional information you would need to know (3) (Total 9 marks) 8

9 5. The diagram below (not to scale) shows the planet Neptune (N) with its two largest moons, Triton (T) and Proteus (P). Triton has an orbital radius of m and that of Proteus is m. The orbits are assumed to be circular. T P N (a) Explain why the velocity of each moon varies whilst its orbital speed remains constant (1) (b) Write down an equation that shows how Neptune s gravitational attraction provides the centripetal force required to hold Triton in its orbit. Hence show that it is unnecessary to know the mass of Triton in order to find its angular speed (3) 9

10 (c) Show that the orbital period of Triton the orbital period of Proteus is approximately (4) (Total 8 marks) 6. NASA wishes to recover a satellite, at present stranded on the Moon s surface, and to place it in orbit around the Moon. (a) (i) The grid below shows a graph of gravitational field strength against distance from the centre of the Moon. Mark on the grid the area that corresponds to the energy needed to move 1 kg from the surface of the Moon to a vertical height of 4000 km above the surface. gravitational field strength/ N kg 1 radius of the Moon = 1700 km distance from centre of Moon/km (ii) The satellite has a mass of 450 kg. Estimate the change in gravitational potential energy of the satellite when it is moved from the surface of the Moon to a vertical height of 4000 km above the surface. (4) 10

11 (b) NASA now decides to bring the satellite back to Earth. Explain why the amount of fuel required to return the satellite to Earth will be much less than the amount required to send it to the Moon originally. Two of the 6 marks for this question are available for the quality of your written communication (6) (Total 12 marks) 11

12 7. The diagram shows the graph of force on a car against time when the car of mass 500kg crashes into a wall without rebounding. 4 force/10 N time/s Which one of the following statements is correct? A B C D The area under the graph is equal to the initial momentum of the car Momentum is not conserved in the collision Kinetic energy is conserved in the collision The average force exerted on the car is N (Total 1 mark) 8. A body is accelerated from rest by a constant force. Which one of the following graphs best represents the variation of the body s momentum p with time t? p p 0 0 A t 0 0 B t p p 0 0 C t 0 0 D t (Total 1 mark) 12

13 9. A body X, moving with a velocity v, collides elastically with a stationary body Y of equal mass. X m Y m velocity = v velocity = 0 Which one of the following correctly describes the velocities of the two bodies after the collision? velocity of X velocity of Y A B v 2 v 2 v v 2 2 C v 0 D 0 v 10. (a) Starting with the relationship between impulse and the change in momentum, show clearly that the unit, N, is equivalent to kg m s (b)... A rocket uses a liquid propellant in order to move. Explain how the ejection of the waste gases in one direction makes the rocket move in the opposite direction (3) 13

14 (c) A rocket ejects kg of waste gas per second. The gas is ejected with a speed of 2.4 km s 1 relative to the rocket. Show that the average thrust on the rocket is about 40 MN (Total 7 marks) 11. A fixed mass of gas is held in the cylinder shown below. It is heated at a constant pressure of Pa. The initial temperature of the gas is 27 C. The cylinder has a cross sectional area of m m 0.16 m (a) Calculate the final temperature of the gas (b) Calculate the work done by the gas as it expands

15 (c) State and explain what would have happened to the gas had it been heated by the same amount at constant volume (3) (Total 7 marks) 12. (a) (i) The internal energy of a gas is the sum of the potential and kinetic energies of the molecules of the gas. Explain why, for an ideal gas, only the kinetic energy changes when the internal energy of the gas is increased either at constant volume or at constant pressure. (3) (ii) Calculate the total kinetic energy of the atoms in mol of an ideal gas at a temperature of 290 K. The Avogrado constant is mol 1. The Boltzmann constant is J K 1 15

16 (b) The laws of football require the ball to have a circumference between 680 mm and 700 mm. Its pressure should be between and Pa above atmospheric pressure at sea level. One ball has a circumference of 690 mm. The molar mass of air is kg mol 1. The universal gas constant R is 8.3 J mol 1 K 1. (i) The thickness of the material used for the ball is negligible. Show that the volume of air in the football is approximately m3. (ii) Assuming that the temperature is 17 C and that the atmospheric pressure at sea level is Pa, calculate the minimum mass of air inside the ball that satisfies the regulation. (3) (iii) Calculate the pressure that would exist in the football if the temperature were to fall to 0 C. Assume that the volume of the ball remains constant. (1) (Total 11 marks) 16

17 13. (a) The first law of thermodynamics may be written as: ΔU = Q + W State the meaning of positive values for each of the symbols in this equation. ΔU... Q... W... (3) (b) For an isothermal change in an ideal gas: (i) explain why ΔU = 0; (1) (ii) explain the effects on Q and W. 17

18 (c) The diagram below shows an isothermal expansion for mol of an ideal gas. p/mpa V/10 m (i) Show that the temperature at which this expansion occurs is approximately 600 K. molar gas constant, R = 8.3 J mol 1 K 1 (ii) Add to the diagram above a second line to show the expansion of the ideal gas at a temperature of 400 K. Show how you have chosen your values. (4) (Total 12 marks) 18

19 14. A meteorite of mass kg enters the Earth s atmosphere at a speed of 2.5 km s 1. (a) Calculate the kinetic energy of the meteorite as it enters the atmosphere (b) The meteorite is initially at a temperature of 25 C. It is made of iron of specific heat capacity 110 J kg 1 K 1 and of melting point 1810 C. As the meteorite travels through the Earth s atmosphere friction causes its temperature to rise. Calculate the energy needed to raise the temperature of the meteorite to its melting point. You should assume that the specific heat capacity of iron remains constant (3) (c) When it reaches the surface of the Earth the mass of the meteorite has fallen to kg and its speed to 150 m s 1 so that its kinetic energy is only J. On striking the Earth this mass penetrates the Earth s crust and is brought to rest in a distance of 25 m. Calculate: (i) the average force acting on the meteorite as it penetrates the Earth s crust; (ii) the time it takes for the meteorite to be brought to rest by the Earth s crust; 19

20 (iii) the rate at which the meteorite dissipates energy in this time. (Total 11 marks) 15. (a) A rocket takes off from the Earth. Exhaust gases are discharged vertically downwards causing the rocket to accelerate vertically upwards. Figure 1 is a sketch graph of the velocity of the rocket against time after lift off. velocity Figure 1 time (i) Describe the acceleration of the rocket during the time shown in Figure 1. (1) (ii) By referring to the graph in Figure 1, explain your answer to (i). (1) (iii) Suggest why the rocket accelerates as you have described. (1) 20

21 (b) A satellite has a mass of kg. Initially, it is placed in an orbit of radius m around the Earth. (i) Show that the centripetal force provided by gravitational attraction is N. universal gravitational constant, G = N m 2 kg 2 mass of the Earth = kg (ii) Figure 2 shows the variation of the gravitational force F on the satellite with orbital radius R. F/10 4 N R/10 m Figure 2 21

22 Show that the data given in Figure 2 are consistent with the inverse square law for the variation of force with distance. (3) (iii) Use data from Figure 2 to find the change in potential energy which occurs when the satellite is raised from its orbit of radius m to an orbit of radius m.... (3) (iv) When the radius of the orbit is m, the centripetal force on the satellite is N. Calculate the speed of the satellite. (v) State and explain whether energy transformed from chemical energy as the fuel burns is equal to the change in potential energy which occurs when the radius of the orbit is increased. (3) (Total 16 marks) 22

23 16. The diagram shows two pendulums suspended from fire same thread, PQ. P Q Y X X is a heavy pendulum, the frequency f x of which can be varied. Y is a lighter pendulum of fixed frequency f y. As the frequency of oscillation of X is increased by shortening the thread, the amplitude of the oscillation of Y changes. Which one of the following graphs best represents the relationship between the amplitude a y of the oscillation of Y and the frequency f x of X? a y a y a y a y f y f x 0 f y f x 0 f y f x 0 f y f x A B C D (Total 1 mark) 17. Figure 1 shows one cycle of the displacement-time graphs for two mass-spring systems X and Y that are performing simple harmonic motion. displacement /m Y X time /s Figure 1 23

24 (a) (i) Determine the frequency of the oscillations. (ii) The springs used in oscillators X and Y have the same spring constant. Using information from Figure 1, show that the mass used in oscillator Y is equal to that in oscillator X. (iii) Explain briefly how you would use one of the graphs in Figure 1 to confirm that the motion is simple harmonic. 24

25 (b) Figure 2 shows how the potential energy of oscillator X varies with displacement. potential energy /J (i) (ii) displacement /m Figure 2 Draw on Figure 2 a graph to show how the kinetic energy of the mass used in oscillator X varies with its displacement. Label this A. Draw on Figure 2 a graph to show how the kinetic energy of the mass used in oscillator Y varies with its displacement. Label this B. (1) (c) Use data from the graphs to determine the spring constant of the springs used (3) (Total 12 marks) 25

26 18. One of the reasons why earthquakes can cause such devastation is that they can cause buildings to resonate. For a multi-storey building it is found that the natural period of oscillation is approximately 0.1 s multiplied by the number of storeys. (a) Explain what is meant by the terms: (i) resonate;... (ii) natural period of oscillation... (b) A typical earthquake oscillation has a frequency of 2.5 Hz. (i) Estimate the number of storeys that a building would have in order to resonate at this frequency. (ii) Sketch a graph of how the displacement of the building might be expected to change with time just after the earthquake had finished. Assume that the building was not damaged by the earthquake. Show three complete cycles. (iii) Explain why a building of one storey more than that in part (b)(i) would be less likely to be damaged by the earthquake. (1) 26

27 (iv) The diagram below shows two buildings of different heights situated close together. Explain why these two buildings are more likely to suffer damage than if they were built further away from each other. (c) When a tall building vibrates at 1.5 Hz, the amplitude of the horizontal oscillations at its top is 1.2 m. Assuming that the vibration is simple harmonic, calculate: (i) the velocity of the top of the building as it passes the rest position; (3) (ii) the acceleration of the top of the building as it reaches the maximum displacement. (Total 16 marks) 27

28 19. The diagrams show the variation of velocity and acceleration with time for a body undergoing simple harmonic motion. velocity acceleration 0 P time 0 Q time Which one of the following is proportional to the change in momentum of the body during the time covered by the graphs? A B C D The area enclosed by the velocity-time graph and the time axis The gradient of the velocity-time graph at the point P The area enclosed by the acceleration-time graph and the time axis The gradient of the acceleration-time graph at the point Q (Total 1 mark) 20. A particle is oscillating with simple harmonic motion described by the equation: s = 5 sin (20πt) How long does it take the particle to travel from its position of maximum displacement to its mean position? A 1 s 40 B 1 s 20 C 1 s 10 D 1 s 5 (Total 1 mark) 28

29 21. Figure 1 shows an apparatus for investigating forced vibrations and resonance of a mass-spring system. Figure 2 shows the displacement-time graph when the system is resonating. cotton attached to the rim cotton displacement/cm +10 rotating wheel driven by a motor spring time/s mass Figure 1 Figure 2 (a) (i) State what is meant by a forced vibration. (1) (ii) Under what condition will resonance occur in the system shown in Figure 1? (1) (b) The spring constant of the spring used in the experiment was 9.0 N m 1. Using information from Figure 2, determine the value of the mass suspended from the spring (3) 29

30 (c) When the rotating wheel stops, Figure 3 shows how the amplitude of the oscillations of the mass subsequently varies with time. amplitude/cm time/s Figure 3 (i) Explain whether the graph supports the suggestion that the amplitude of the damped oscillations varies exponentially with time. Show your reasoning clearly. (3) (ii) Determine the ratio: energy of the oscillator after twenty oscillations energy of the oscillator at timet = 0 (Total 10 marks) 30

31 22. The diagram below shows how the kinetic energy of a simple pendulum varies with displacement. 2 energy/10 J displacement/m (a) Sketch on the diagram above a graph to show how the potential energy of the pendulum varies with displacement. (b) (i) State the amplitude of the oscillation. (1) (ii) The frequency of vibration of the pendulum is 3.5 Hz. Write down the equation that models the variation of position with time for the simple harmonic motion of this pendulum. (1) (iii) Calculate the maximum acceleration of the simple pendulum. (Total 6 marks) 31

32 23. Figure 1 shows a mass suspended on a spring. fixed support Figure 1 The mass is pulled down by a distance A below the equilibrium position and then released at time t = 0. It undergoes simple harmonic motion. (a) Taking upward displacements as being positive, draw graphs on Figure 2 to show the variation of displacement, velocity and the acceleration with time. Use the same time scale for each of the three graphs. displacement 0 time velocity 0 time accelaration 0 time Figure 2 (4) 32

33 (b) The spring stiffness, k, is 32 N m 1. The spring is loaded with a mass of 0.45 kg. Calculate the frequency of the oscillation (3) (Total 7 marks) 24. (a) State the conditions necessary for a mass to undergo simple harmonic motion (b) A child on a swing oscillates with simple harmonic motion of period 3.2 s. acceleration of free fall = 9.8ms 2 (i) Calculate the distance between the point of support and the centre of mass of the system. 33

34 (ii) The total energy of the oscillations is 40 J when the amplitude of the oscillations is 0.50 m. Sketch a graph showing how the total energy of the child varies with the amplitude of the oscillations for amplitudes between 0 and 1.00 m. Include a suitable scale on the total energy axis. total energy/j amplitude/m 34

35 25. (a) Simple harmonic motion may be represented by the equation a = (2πf) 2 x (i) Explain the significance of the minus sign in this equation. (1) (ii) In Figure 1 sketch the corresponding v-t graph to show how the phase of velocity v relates to that of the acceleration a. a 0 0 t v 0 0 t (1) (b) (i) A mass of 24 kg is attached to the end of a spring of spring constant 60 N m 1. The mass is displaced m vertically from its equilibrium position and released. Show that the maximum kinetic energy of the mass is about 40 mj. (5) 35

36 (ii) When the mass on the spring is quite heavily damped its amplitude halves by the end of each complete cycle. On the grid of Figure 2 sketch a graph to show how the kinetic energy, E k, of the mass on the spring varies with time over a single period. Start at time, t = 0, with your maximum kinetic energy. You should include suitable values on each of your scales. E /mj k 0 0 t/s (3) (Total 10 marks) 36

37 26. To simulate the high accelerations experienced during take-off, astronauts are trained using a system similar to the one shown in the figure below m plate bolted to cabin rotating vertical shaft The astronaut sits, as shown, and the system is accelerated to a high speed. The centre of mass of the astronaut is 20.0 m from the axis of rotation. (a) Explain why there is a horizontal force on the astronaut, even when the speed is constant (3) (b) Write down the formula for the horizontal force on the astronaut, defining all the terms used (1) 37

38 (c) In one test the astronaut experiences a horizontal force 4.0 times that due to normal gravity. Determine the speed of the astronaut during this test. acceleration due to gravity g = 9.8 m s (Total 6 marks) 27. A gymnast does a hand-stand on a horizontal bar. The gymnast then rotates in a vertical circle with the bar as a pivot. The gymnast and bar remain rigid during the rotation and when friction and air resistance are negligible the gymnast returns to the original stationary position. Figure 1 shows the gymnast s position at the start and Figure 2 shows the position after completing half the circle. direction of subsequent motion horizontal bar horizontal bar direction of motion Figure 1 Figure 2 (a) The gymnast has a mass of 70 kg and the centre of mass of the gymnast is 1.20 m from the axis of rotation. acceleration of free fall, g = 9.8 m s 2 (i) Show clearly how the principle of conservation of energy predicts a speed of 6.9 m s 1 for the centre of mass when in the position shown in Figure 2. (3) 38

39 (ii) The maximum force on the arms of the gymnast occurs when in the position shown in Figure 2. Calculate the centripetal force required to produce circular motion of the gymnast when the centre of mass is moving at 6.9 m s 1. (iii) Determine the maximum tension in the arms of the gymnast when in the position shown in Figure 2. (1) (iv) Sketch a graph to show how the vertical component of the force on the bar varies with the angle rotated through by the gymnast during the manoeuvre. Assume that a downward force is positive. Include the values for the initial force and the maximum force on the bar. Only show the general shape between these values. force/n angles/degrees 39

40 (b) The bones in each forearm have a length of 0.25 m. The total cross-sectional area of the bones in both forearms is m 2. The Young modulus of bone in compression is Pa. Assuming that the bones carry all the weight of the gymnast, calculate the reduction in length of the forearm bones when the gymnast is in the start position shown in Figure (3) (Total 11 marks) 40

41 Use this information to answer questions 28/29/30 Mineral prospecting Exploration for new ore deposits by drilling holes in the Earth can be a costly hit and miss exercise. The geophysicist employs physics to search for the location of ore deposits. The techniques used come from almost all branches of physics. Optical and infrared satellite photographs are first used to identify likely areas for further tests. Experiments are then carried out to investigate variations in one or usually several physical factors. For example, ores may produce local variations in the strength of the Earth s magnetic field, in the strength of the Earth s gravitational attraction, in the electrical resistivity of the Earth, in the speed of waves through the Earth (seismology) or, for radioactive ores, in the count rate measured using a radiation detector. Voltage measurements to detect variation in resistivity These measurements use the principle of the potential divider. Two methods are commonly used. In the method shown in Figure 1, a battery is connected to two electrodes A and B which are inserted in the ground some distance apart, ensuring good electrical contact between the electrodes and the soil. V A C B 20 m Figure 1 V A P Q B 0.50 m 20 m Figure 2 A test electrode C is then moved along the line joining the electrodes and the potential difference between A and C is measured. The geophysicist plots a graph of voltage against the distance. If the soil is of uniform resistivity the voltage increases linearly. Where there is an ore body, ions are released into the soil and this changes the gradient of the graph. The graph in Figure 3 shows the results of one test using the method in Figure 1. 41

42 In the alternative approach, shown in Figure 2, two electrodes, P and Q, placed 0.50 m apart are moved along the line between the electrodes A and B, and the variation of the voltage with position is used to locate the ore deposit. Seismology In seismology a small explosion is produced at the surface (X in Figure 4) and the electric pulse which causes the explosion is used to start a clock. The explosion sends a shock wave through the ground to a geophone some distance away (at Y). potential difference between A and C/ V distance AC /m Figure 3 clock start clock clock stop geophone X ground Y 42

43 terminal magnet case coil fixed to case spring spike to be inserted into the ground Figure 4 Figure 5 The structure of the geophone (simplified) is shown in Figure 5. The shock wave makes the coil in the geophone move up and down inducing a voltage which is used to stop the clock. The time taken for the wave to travel the distance XY is then known so that the speed of the shock wave between X and Y can be calculated. The speed of the shock wave changes from about 2000 m s 1 in soft soil to over 4000 m s 1 in ore deposits. 43

44 28. (a) State the factors that affect the gravitational field strength at the surface of a planet (b) The diagram below shows the variation, called an anomaly, of gravitational field strength at the Earth s surface in a region where there is a large spherical granite rock buried in the Earth s crust. gravitational field strength normal gravitational field strength N kg distance from A/km A B Earth's surface granite rock 0.60 distance below Earth's surface/km The density of the granite rock is 3700 kg m 3 and the mean density of the surrounding material is 2200 kg m 3. 44

45 (i) Show that the difference between the mass of the granite rock and the mass of an equivalent volume of the surrounding material is kg. (4) (ii) The universal gravitational constant G = N m 2 kg 2. Calculate the difference between the gravitational field strength at B and that at point A on the Earth s surface that is a long way from the granite rock. (4) (iii) Add to the diagram above a graph to show how the variation in gravitational field strength would change if the granite rock were buried deeper in the Earth s crust. (1) (Total 11 marks) 29. The following questions refer to the paragraphs on Resistance or voltage measurements. (a) State what is meant by the phrase good electrical contact.... (1) (b) The graph in Figure 3 shows the results of one test using the method in Figure 1. (i) State and explain whether you would recommend drilling nearer to A or nearer to B. 45

46 (ii) Determine the approximate distance of the edge of the ore body from A. (1) (iii) Determine the terminal potential difference of the supply used in the test that produced the data in Figure 3. (1) (iv) The current through the battery was 5.0 ma. Calculate the resistance between the terminals A and B. (c) Sketch the graph that would be obtained for the region between AB when the circuit in Figure 2 is used. Include a suitable scale on the axes. (3) (Total 10 marks) 46

47 30. The following questions refer to the paragraphs on Seismology. Explain: (a) why movement of the Earth s surface makes the magnet in Figure 5 move relative to the coil; (b) (c) why relative movement between the magnet and the coil produces a voltage; how energy is transmitted by a shock wave and suggest why the speed of the shock wave is different in soft soil and in ore deposits You can gain up to 2 marks in this question for good written communication (3)... (6) (Total 11 marks) 47

48 31. The diagram shows two wires, P and Q, of equal length, joined in series with a cell. A voltmeter is connected between the end of Q and a point X on the wires. The pd across the cell is V. Wire Q has twice the area of cross-section and twice the resistivity of wire P. The variation of the voltmeter reading as the point X is moved along the wires is best shown by V P X Q V A V 0 0 B V 0 0 C V 0 0 D V 0 0 (Total 1 marks) 48

49 32. A strip of aluminium foil of uniform thickness is cut to the shape shown in Figure 1. Current flows through the foil when a potential difference is applied between its ends. A x x 3 B (a) Figure 1 Name the charge carriers responsible for the electrical conduction in aluminium.... (1) (b) Figure 1 shows two points A and B in the regions of different width. The width at B is one-third of the width at A. v A is the charge carrier drift speed at point A and v B is the charge carrier drift speed at point B. (i) State the relationship between the current at point A and the current at point B. (1) (ii) Calculate the ratio of charge carrier drift speeds, vb/va. (c) The foil is connected into an electrical circuit as shown in Figure 2. The power supply has a negligible internal resistance and a constant emf A Figure 2 49

50 State and explain how the current measured by the ammeter will change when the temperature of the foil increases. Two of the 7 marks in this question are available for the quality of your written communication (7) (Total 11 marks) 33. The figure below shows a circuit from which different potential differences can be obtained by making connections to any two of the terminals A, B and C, and by changing the value of the variable resistor (R 2 ). You may assume that the supply has no internal resistance. + 12V R R Ω 0-20 Ω A B C (a) What is the name given to this type of circuit?... (1) (b) What is the value of the potential difference across AC?... (1) 50

51 (c) Calculate the range of potential differences that can be obtained across AB (d) Calculate the range of potential differences that can be obtained across BC (Total 6 marks) 34. The magnetic flux threading a coil of 100 turns drops from Wb to zero in 0.1 s. The average induced emf, in V, is A 0.05 B 0.5 C 5 D 20 (Total 1 mark) 51

52 35. (a) Explain what is meant by a flux density of 1 tesla (T) (1) (b) Complete the diagram below to show a current balance, which may be used to measure the magnetic flux density between the poles of the ceramic magnets. Clearly label the directions of the current and the magnetic force acting on the conductor in the field. ceramic magnet steel yoke (3) (c) (i) The armature of a simple motor consists of a square coil of 20 turns and carries a current of 0.55 A just before it starts to move. The lengths of the sides of the coil are 0.15 m and they are positioned perpendicular to a magnetic field of flux density 40 mt. Calculate the force on each side of the coil. (ii) Explain why the current falls below 0.55 A once the coil of the motor is rotating. 52

53 (iii) The resistance of the coil is 0.50 Ω. When the coil is rotating at a constant rate the minimum current in the coil is found to be 0.14 A. Calculate the maximum rate at which the flux is cut by the coil. (4) (Total 12 marks) 36. Faraday s law of electromagnetic induction predicts that the induced emf, E, in a coil is given Δ( N φ) by E =. t (a) (i) What quantity does the symbol φ represent? (1) (ii) State the SI unit for φ. (1) 53

54 (b) In Figure 1 the magnet forms the bob of a simple pendulum. The magnet oscillates with a small amplitude along the axis of a 240 turn coil that has a crosssectional area of m magnet 1.1 S N direction of oscillation 240 turn coil time / s E Figure 2 Figure time / s Figure 3 Figure 2 shows how the magnetic flux density, B, through the coil varies with time, t, for one complete oscillation of the magnet. The magnetic flux density through the coil can be assumed to be uniform. (i) Calculate the maximum emf induced in the coil. (ii) Sketch on Figure 3 a graph to show how the induced emf in the coil varies during the same time interval. (3) 54

55 (iii) Explain how the pendulum may be modified to double the frequency of oscillation of the magnet. (iv) The frequency of oscillation of the magnet is increased without changing the amplitude. Explain why this increases the maximum induced emf. (v) State two other ways of increasing the maximum induced emf. (vi) Explain how the output from the coil would have to be processed in order to store the information in a computer memory. (Total 15 marks) 55

56 37. Bone can be distinguished from soft tissue on a medical X-ray photograph of the human body. Explain how the bones and soft tissues affect the X-rays to cause this effect (Total 2 marks) 38. (a) State and explain the benefits and drawbacks of X-rays compared with other technologies when used for medical diagnosis. Two of the 7 marks in this question are available for the quality of your written communication

57 (7) (b) (i) State a medical diagnostic technique that overcomes one of the limitations of X-rays that you mentioned. Diagnostic technique... (1) (ii) Explain how the diagnostic technique you stated in part (b)(i) overcomes the limitation of X-rays. (1) 57

58 38. Figures 1a and 1b each show a ray of light incident on a water-air boundary. A, B, C and D show ray directions at the interface. A C air water B D air water Figure 1a Figure 1b (a) Circle the letter below that corresponds to a direction in which a ray cannot occur. A B C D (1) (b) Circle the letter below that corresponds to the direction of the faintest ray. A B C D (1) 58

59 hij Teacher Resource Bank GCE Physics B: Physics in Context Additional Sample Questions (Specification B) Mark Scheme PHYB4 Physics Inside and Out The Assessment and Qualifications Alliance (AQA) is a company limited by guarantee registered in England and Wales (company number ) and a registered charity (registered charity number ). Registered address: AQA, Devas Street, Manchester M15 6EX. Dr Michael Cresswell, Director General.

60 Teacher Resource Bank / GCE Physics / PHYB4 Sample Questions B Mark Scheme / Version (a) (i) acceleration is increasing 1 (ii) slope increases with time 1 (iii) the gravitational field strength is reducing / the mass is reducing 1 (b) (i) F = GMm 2 R 11 3 correct substitution (ii) makes appropriate calculation from one data set eg FR 2 M1 makes appropriate calculation from another data set M1 shows that the two are equal A1 3 (iii) determines area under curve C1 approximately 12 cm squares or 1 cm square is J J A1 3 (iv) F = mv 2 /r C m s 1 A1 2 (v) potential energy is increased there is a change in KE too KE is reduced chemical change not equal to PE change because of KE change relevant, correct comment about energy losses Max 3 [16] 24 C1 2. C 1 [1] GM 3. (a) force acting per unit mass or g = F / m or g = 2 with terms defined R 1 (b) (i) direction of F E correct in each diagram 1 direction of F M correct in each diagram 1 direction of F S correct in each diagram 1 Fs must be distinguished from F M (ii) penalty of 1 mark for any missing labelling 3 sun and moon pulling in same direction / resultant of F M and F s is greatest / clear response including summation of F M and F s M1 1 configuration A A

61 Teacher Resource Bank / GCE Physics / PHYB4 Sample Questions B Mark Scheme / Version 1.0 (c) F = GMm/R 2 C correct substitution ( ) C1 1 (5.95 or 5.96 or 5.9 or 6.0) 10 3 N kg 1 A1 1 3 [9] 4. (a) (i) F = 2500 or 2600 N (ii) F = mv 2 /r 1500 m s 1 / 1480 m s 1 or any further progress towards a solution such as attempting to use: F=GMm/r 2 or ½ mv 2 = mgh or equations of motion or r= or F = mv 2 /(r+h) or evidence of time wasted, for example, repeated attempts at a solution no unit penalty or s.f. penalty 3 using the area under the graph between 0 and m or use of V G = GM/r or PE = GMm/r between 20 and 22 squares or 1 square = 10 8 J or uses the trapezium rule or rectangle and triangle (allow if they fail with powers of ten) or attempts to find the difference between the 2 values of PE J to J or attempt to complete the calculation (may be confounded by lack of r) A1 3 (b) (work done by motors) relates to change in PE or (PE + KE) 2 (PE + KE) condone 2 (PE) need to know energy value of fuel / fuel density / energy density of fuel / fuel economy / efficiency of engines 3 [9] C1 C1 5. (a) direction changing, velocity vector 1 (b) Newton s law equation M1 centripetal force equation M1 cancel mass of Triton A1 3 (c) ω = 2 πf or ω = 2 π/t M1 ω 2 r 3 = constant or ω 2 GM = 3 r M1 3

62 Teacher Resource Bank / GCE Physics / PHYB4 Sample Questions B Mark Scheme / Version T 2 P 3 T 3 P T r = or statement of Kepler III for B3 M1 4 T T T T P r ( = 8 3 ( ) ) 3 [8] 6. (a) (i) Endpoint 1700 Endpoint (ii) counts squares [100 ± 10] evaluates energy/kg of one square [ J/kg] computes total energy for 1 kg C1 multiplies by 450 accept range J J A1 4 (b) 7. A or Combines correct equations Read off from graph correct for g or quotes correct value Calculation correct Multiplies by 450 [ans: J] Compares correctly up to 3 of Gravitational potential (energy) Grav field (strength)/g/force of gravity/gravitational attraction Escape velocity Kinetic energy not energy bald Distance to neutral point OWTTE Fuel weight at launch/launch vehicle size (large first stage at Earth) Plus States earth mass > moon mass B2 Quotes both values of g earth (9.8 N/kg) and g moon (1.7 N/kg) to 2sf or 6:1 ratio expressed unambiguously Max 4 Use of Physics terms is accurate, the answer is fluent/well argued with few errors in spelling, punctuation and grammar B2 And gains at least 2 marks for Physics Use of Physics terms is accurate but the answer lacks coherence or the spelling, punctuation and grammar are poor and gains at least 1 mark for Physics Use of Physics terms is inaccurate, the answer is disjointed with significant errors in spelling, punctuation and grammar B0 [12] C1 A1 B3 [1] 8. B 9. D [1] [1] 4

63 Teacher Resource Bank / GCE Physics / PHYB4 Sample Questions B Mark Scheme / Version (a) Δ(mv) F = t or Ft = mv mu etc. M1 substitute units A1 2 (b) conservation of momentum mentioned ejected gas has momentum or velocity in one direction rocket must have equal momentum in the opposite direction 3 or force = rate of change of momentum ejected gas has momentum or velocity in one direction rocket must have equal and opposite force () () () (c) equation seen (F = m/t v but not F= ma) substitution into any sensible equation leading to (N) 2 [7] 11. (a) use of V/T = constant C1 127 C A1 2 (b) W = pδv C1 45 J A1 2 (c) higher temperature greater pressure internal energy greater as no work done by the gas 3 [7] 12 (a) (i) the molecules of an ideal gas are assumed not to attract one another or negligible attractive force molecules of an ideal gas have no internal potential energy no work is done in separating molecules at constant pressure KE increases as the molecules move faster increasing the KE Max 3 (ii) 3/2 kt seen in a calculation (3/ ) or energy of 1 molecule = J or seen in calculation or number of molecules = C J A1 1 (b) (i) calculation of radius using circumference = 2πr (110 mm) r = 0.690/2π seen in calculation 1 calculation of volume using 4/3 πr 3 (must see evidence: either substitution of radius in equation or a calculated value to 3 sf) 1 (ii) use of T = 290 K or pressure = Pa in pv =nrt C1 1 number of moles =PV/RT= mol (0.23 mol common) A1 1 mass = = g (ecf common incorrect answer is 6.5) 1 m p V = 8.3T with correct p or T gets 2 28 (iii) Pa (ecf common answer with ecf is Pa) 1 [11] 5

64 Teacher Resource Bank / GCE Physics / PHYB4 Sample Questions B Mark Scheme / Version (a) increase in internal energy 1 heat / thermal energy supplied to the system or energy supplied to system by heating 1 work done on the system 1 (b) (i) constant temperature 1 (ii) heat supplied to system = work done by system (or on surroundings) 1 work done on the system = heat transferred to surroundings (or from system) 1 (c) (i) pv = nrt M1 1 choice of point on curve and correct substitution giving e.g., 602(K) or 581(K) (all half a small square tolerance) A1 1 (ii) smooth curve below first curve not touching curve of axes 1 correct point (need not be marked as dot provided curve passes through correct point e.g. (0.2, 2)) 1 2 nd correct point e.g. (0.4.,1) 1 supporting evidence e.g., p 1 V 1 or pv = 4 (=3.98) 1 [12] 14. (a) ½ mv 2 or substitution ignoring powers of 10 C J A 1 (b) Q = mcδθ C seen C J A1 1 (c) (i) W = Fs or correctly substituted values C N A1 1 condone effect of change of g.p.e. (ii) force = rate of change of momentum or use of an equation of motion C s A1 1 (iii) P = W/t or P = Fv or substitution ignoring powers of 10 C (or 1.86) 10 8 W e.c.f. from (c)(ii) A1 1 [11] 15. (a) (i) acceleration is increasing 1 (ii) slope increases with time 1 (iii) the gravitational field strength is reducing / the mass is reducing 1 (b) (i) F = GMm 2 R 11 3 correct substitution (ii) makes appropriate calculation from one data set eg FR 2 M1 makes appropriate calculation from another data set M1 shows that the two are equal A1 3 (iii) determines area under curve C1 24 6

65 Teacher Resource Bank / GCE Physics / PHYB4 Sample Questions B Mark Scheme / Version C approximately 12 cm squares or 1 cm square is J J A1 3 (iv) F = mv 2 /r C m s 1 A1 2 (v) potential energy is increased there is a change in KE too KE is reduced chemical change not equal to PE change because of KE change relevant, correct comment about energy losses Max 3 [16] C1 [1] 17. (a) (i) period = 1.2 s or T = l/f C Hz or A1 2 (ii) period /frequency is the same or T l = T 2 since T depends on k m or T = 2π k m and k is constant 2 (iii) waveform sinusoidal or fits x = A sin ω t (accept cos waveform) M1 A after 1/8 cycle should be A/ 2 or find ω (= 2πf) and A; calculate x at any time and compare A1 or use gradients to plot v t then a t graphs M1 check whether s a for all t is constant A1 2 (b) (i) correct curvature with values at ends and centre correct and crossing at 0.08 ± 1 small square both sides 1 (ii) correct curvature M0 end displacements correct (1/2 that for X i.e. 0.1) A1 maximum correct (1/4 that for X i.e ± 1 small square) A1 2 (c) reads maximum energy and displacement correctly 0.16 J and 0.20 m (allow e.c.f. for (b)(i) and (b)(ii)) C quotes E = kδχ or E = Fx and F= kx 2 2 C1 correct substitution leading to a value for k (8.0 N m 1 ) A1 or maximum speed of oscillator X = ωa C1 (using maximum gradient 0.2/0.15 or 27πfA (1.04 ms 1 )) mass of oscillator from E m = ½ mv 2 gives kg (v = 1.04 gives kg) T = 2π k m leading to a value for k (k = 5.2 Nm 1 ) A1 (v = 1.04 gives 8.1 N m 1 ) C1 7

66 Teacher Resource Bank / GCE Physics / PHYB4 Sample Questions B Mark Scheme / Version 1.0 (discrepancy due to difficulty of measuring gradient) 3 [12] 18. (a) (i) mention of large amplitude or maximum energy mention of applied frequency being matched to natural frequency of building C 20. A 1 (ii) time for one oscillation or T = f n T n or f n when no forcing frequency applied consistently 2 (b) (i) 0.4 or use of f = 1/T C1 4 storeys A1 2 (ii) 3 cycles shown, constant period, T = 0.4 s or T shown on graph decay in amplitude 2 (iii) applied frequency no longer = natural frequency not just no longer resonates ; allow now T = 0.5 s 1 (iv) 2 possible resonant frequencies collisions between two buildings or one collapses on other 2 2π (c) (i) ω = 2πf or ω = or ω = 9.4 T C1 v = ωa or equivalent C m s 1 A1 3 (ii) a = ω 2 A C1 107(106) m s 2 (e.c.f. for ω from (c)(i)) A1 2 [16] 21. (a) (i) system made to oscillate by a periodic external force / energy source or system made to oscillate by another oscillator it is connected to or another oscillator forcing the system to vibrate or an oscillator forcing another oscillator to vibrate due to its own vibrations 1 (ii) not made to oscillate by an external force not when its vibrations are not at its natural frequency not when it is made to oscillate by another system frequency of wheel (motor)= natural frequency of system condone fundamental or resonant frequency of the system or rotating wheel rotates at the resonant / fundamental frequency of the system 1 must be reference to the wheel or motor or driver oscillator not just when it vibrates at its natural frequency [1] [1] 8

67 Teacher Resource Bank / GCE Physics / PHYB4 Sample Questions B Mark Scheme / Version 1.0 (b) T = 1.25 s T = 2π(m/k) 1/2 or numerical substitution C kg A1 allow e.c.f. for T; 0.6 s gives 0.82 kg 3 (c) (i) correct process using ratios (eg times to halve marked on the graph) three amplitudes read correctly or two times to halve read correctly ratios determined and conclusion drawn that it is exponential or a clear statement that the time to halve is the same for points indicated and conclusion that it is exponential 3 (ii) amplitude correct for 25 s, i.e. 4 to 4.2 cm or energy proportional to A 2 (allow 0.5 ka 2 or 0.5 kx 2 ) C1 allow e.c.f. from (b); T = 0.6 s leads to amplitude = 6.8 cm ; ratio = or 17/100 (2 s.f. only) A1 2 [10] 22. (a) Max to zero to max with zero at 0 displacement and correct amplitude M1 correct shape drawn with reasonable attempt to keep total energy constant, crossing at 1 x 10-2 J A1 2 (b) (i) m 1 (ii) x = cos 2π3.5t (0.044 cos 22t) or x = sin 2π3.5t etc ecf for A 1 (iii) α max = (2 π 3.5) C1 21 (21.3) m s -2 ecf for A and incorrect 2πf from (ii) A1 (0.042 gives 20.3; 0.04 gives 19.4) 2 [6] 23. (a) displacement negative cosine 1 velocity consistent with first graph 1 acceleration consistent with first or second graph 1 at least one cycle, constant amplitude (condone small decay ), include A for displacement, reasonably drafted 1 (b) use of T = 2π m i.e. substituted values or 0.74 seen k C1 1 1 use or implied use of T = f C Hz A1 1 [7] 9

68 Teacher Resource Bank / GCE Physics / PHYB4 Sample Questions B Mark Scheme / Version (a) acceleration/force is directed toward a (fixed) point/the centre/the equilibrium position or a = kx + means that a is opposite direction to x acceleration/force is proportional to the distance from the point/displacement or a = kx where a = acceleration; x = displacement and k is constant 2 (b) (i) 3.2 = 2π l/9.8 (condone use of g = 10 m s 2 for C mark) (use of a = ω 2 x is a PE so no marks) C1 2.5(4) m A1 2 (ii) Correct value at 0.5 m and correct curvature M1 Energy at 1 m = 160 J A1 2 [6] 25. (a) (i) acceleration (not a) and displacement (not x) are in opposite directions OR restoring force/acceleration always acts toward rest position 1 (ii) (+) sine curve consistent with a graph 1 (b) (i) statement that E K = E P statement of max values considered E P = ½ k(δl) 2 or E Pmax = ½ ka 2 correctly substituted values E K = J OR f = 1/T or T = 3.97 s or period equation leading to f = Hz ω max = 1.58 rad s 1 or v max = 0.055ms 1 (seen or used) substituted values into E K = ½mA 2 ω 2 or E K = ½mv 2 E K = J 5 (ii) any attenuation from t=0 seen M1 10 mj or E 0 /4 at either 4s or third hump M1 consistent period values minima at 1 and 3s maxima at 0 and 4s A1 3 [10] 26. (a) velocity is vector velocity is changing there is an acceleration or mention of centripetal force 3 (b) F = mv 2 / r with terms defined 1 (c) acceleration = v 2 / r C1 28 m s 1 A1 2 [6] 10

the total number of electrons passing through the lamp.

the total number of electrons passing through the lamp. 1. A 12 V 36 W lamp is lit to normal brightness using a 12 V car battery of negligible internal resistance. The lamp is switched on for one hour (3600 s). For the time of 1 hour, calculate (i) the energy

Διαβάστε περισσότερα

Potential Dividers. 46 minutes. 46 marks. Page 1 of 11

Potential Dividers. 46 minutes. 46 marks. Page 1 of 11 Potential Dividers 46 minutes 46 marks Page 1 of 11 Q1. In the circuit shown in the figure below, the battery, of negligible internal resistance, has an emf of 30 V. The pd across the lamp is 6.0 V and

Διαβάστε περισσότερα

[1] P Q. Fig. 3.1

[1] P Q. Fig. 3.1 1 (a) Define resistance....... [1] (b) The smallest conductor within a computer processing chip can be represented as a rectangular block that is one atom high, four atoms wide and twenty atoms long. One

Διαβάστε περισσότερα

PhysicsAndMathsTutor.com 1

PhysicsAndMathsTutor.com 1 PhysicsAndMathsTutor.com 1 Q1. The magnetic flux through a coil of N turns is increased uniformly from zero to a maximum value in a time t. An emf, E, is induced across the coil. What is the maximum value

Διαβάστε περισσότερα

Math 6 SL Probability Distributions Practice Test Mark Scheme

Math 6 SL Probability Distributions Practice Test Mark Scheme Math 6 SL Probability Distributions Practice Test Mark Scheme. (a) Note: Award A for vertical line to right of mean, A for shading to right of their vertical line. AA N (b) evidence of recognizing symmetry

Διαβάστε περισσότερα

HOMEWORK 4 = G. In order to plot the stress versus the stretch we define a normalized stretch:

HOMEWORK 4 = G. In order to plot the stress versus the stretch we define a normalized stretch: HOMEWORK 4 Problem a For the fast loading case, we want to derive the relationship between P zz and λ z. We know that the nominal stress is expressed as: P zz = ψ λ z where λ z = λ λ z. Therefore, applying

Διαβάστε περισσότερα

Capacitors - Capacitance, Charge and Potential Difference

Capacitors - Capacitance, Charge and Potential Difference Capacitors - Capacitance, Charge and Potential Difference Capacitors store electric charge. This ability to store electric charge is known as capacitance. A simple capacitor consists of 2 parallel metal

Διαβάστε περισσότερα

CHAPTER 25 SOLVING EQUATIONS BY ITERATIVE METHODS

CHAPTER 25 SOLVING EQUATIONS BY ITERATIVE METHODS CHAPTER 5 SOLVING EQUATIONS BY ITERATIVE METHODS EXERCISE 104 Page 8 1. Find the positive root of the equation x + 3x 5 = 0, correct to 3 significant figures, using the method of bisection. Let f(x) =

Διαβάστε περισσότερα

(1) Describe the process by which mercury atoms become excited in a fluorescent tube (3)

(1) Describe the process by which mercury atoms become excited in a fluorescent tube (3) Q1. (a) A fluorescent tube is filled with mercury vapour at low pressure. In order to emit electromagnetic radiation the mercury atoms must first be excited. (i) What is meant by an excited atom? (1) (ii)

Διαβάστε περισσότερα

In your answer, you should make clear how evidence for the size of the nucleus follows from your description

In your answer, you should make clear how evidence for the size of the nucleus follows from your description 1. Describe briefly one scattering experiment to investigate the size of the nucleus of the atom. Include a description of the properties of the incident radiation which makes it suitable for this experiment.

Διαβάστε περισσότερα

PHYA4/2. (JUN14PHYA4201) WMP/Jun14/PHYA4/2/E4. General Certificate of Education Advanced Level Examination June 2014

PHYA4/2. (JUN14PHYA4201) WMP/Jun14/PHYA4/2/E4. General Certificate of Education Advanced Level Examination June 2014 Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials Physics A General Certificate of Education Advanced Level Examination June 2014 PHYA4/2 Question

Διαβάστε περισσότερα

Figure 1 T / K Explain, in terms of molecules, why the first part of the graph in Figure 1 is a line that slopes up from the origin.

Figure 1 T / K Explain, in terms of molecules, why the first part of the graph in Figure 1 is a line that slopes up from the origin. Q1.(a) Figure 1 shows how the entropy of a molecular substance X varies with temperature. Figure 1 T / K (i) Explain, in terms of molecules, why the entropy is zero when the temperature is zero Kelvin.

Διαβάστε περισσότερα

Mean bond enthalpy Standard enthalpy of formation Bond N H N N N N H O O O

Mean bond enthalpy Standard enthalpy of formation Bond N H N N N N H O O O Q1. (a) Explain the meaning of the terms mean bond enthalpy and standard enthalpy of formation. Mean bond enthalpy... Standard enthalpy of formation... (5) (b) Some mean bond enthalpies are given below.

Διαβάστε περισσότερα

Nuclear Physics 5. Name: Date: 8 (1)

Nuclear Physics 5. Name: Date: 8 (1) Name: Date: Nuclear Physics 5. A sample of radioactive carbon-4 decays into a stable isotope of nitrogen. As the carbon-4 decays, the rate at which the amount of nitrogen is produced A. decreases linearly

Διαβάστε περισσότερα

Phys460.nb Solution for the t-dependent Schrodinger s equation How did we find the solution? (not required)

Phys460.nb Solution for the t-dependent Schrodinger s equation How did we find the solution? (not required) Phys460.nb 81 ψ n (t) is still the (same) eigenstate of H But for tdependent H. The answer is NO. 5.5.5. Solution for the tdependent Schrodinger s equation If we assume that at time t 0, the electron starts

Διαβάστε περισσότερα

titanium laser beam volume to be heated joint titanium Fig. 5.1

titanium laser beam volume to be heated joint titanium Fig. 5.1 1 Lasers are often used to form precision-welded joints in titanium. To form one such joint it is first necessary to increase the temperature of the titanium to its melting point. Fig. 5.1 shows the joint

Διαβάστε περισσότερα

Απόκριση σε Μοναδιαία Ωστική Δύναμη (Unit Impulse) Απόκριση σε Δυνάμεις Αυθαίρετα Μεταβαλλόμενες με το Χρόνο. Απόστολος Σ.

Απόκριση σε Μοναδιαία Ωστική Δύναμη (Unit Impulse) Απόκριση σε Δυνάμεις Αυθαίρετα Μεταβαλλόμενες με το Χρόνο. Απόστολος Σ. Απόκριση σε Δυνάμεις Αυθαίρετα Μεταβαλλόμενες με το Χρόνο The time integral of a force is referred to as impulse, is determined by and is obtained from: Newton s 2 nd Law of motion states that the action

Διαβάστε περισσότερα

PhysicsAndMathsTutor.com

PhysicsAndMathsTutor.com PhysicsAndMathsTutor.com June 2005 1. A car of mass 1200 kg moves along a straight horizontal road. The resistance to motion of the car from non-gravitational forces is of constant magnitude 600 N. The

Διαβάστε περισσότερα

Strain gauge and rosettes

Strain gauge and rosettes Strain gauge and rosettes Introduction A strain gauge is a device which is used to measure strain (deformation) on an object subjected to forces. Strain can be measured using various types of devices classified

Διαβάστε περισσότερα

Section 9.2 Polar Equations and Graphs

Section 9.2 Polar Equations and Graphs 180 Section 9. Polar Equations and Graphs In this section, we will be graphing polar equations on a polar grid. In the first few examples, we will write the polar equation in rectangular form to help identify

Διαβάστε περισσότερα

Review Test 3. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Review Test 3. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Review Test MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the exact value of the expression. 1) sin - 11π 1 1) + - + - - ) sin 11π 1 ) ( -

Διαβάστε περισσότερα

Homework 3 Solutions

Homework 3 Solutions Homework 3 Solutions Igor Yanovsky (Math 151A TA) Problem 1: Compute the absolute error and relative error in approximations of p by p. (Use calculator!) a) p π, p 22/7; b) p π, p 3.141. Solution: For

Διαβάστε περισσότερα

Volume of a Cuboid. Volume = length x breadth x height. V = l x b x h. The formula for the volume of a cuboid is

Volume of a Cuboid. Volume = length x breadth x height. V = l x b x h. The formula for the volume of a cuboid is Volume of a Cuboid The formula for the volume of a cuboid is Volume = length x breadth x height V = l x b x h Example Work out the volume of this cuboid 10 cm 15 cm V = l x b x h V = 15 x 6 x 10 V = 900cm³

Διαβάστε περισσότερα

What is meter P measuring?... What is meter Q measuring?...

What is meter P measuring?... What is meter Q measuring?... 1 The diagram shows an electrical circuit. (a) (b) Complete the two labels on the diagram. P and Q are meters. What is meter P measuring?... What is meter Q measuring?... (Total 4 marks) Page 1 of 24 2

Διαβάστε περισσότερα

3.4 SUM AND DIFFERENCE FORMULAS. NOTE: cos(α+β) cos α + cos β cos(α-β) cos α -cos β

3.4 SUM AND DIFFERENCE FORMULAS. NOTE: cos(α+β) cos α + cos β cos(α-β) cos α -cos β 3.4 SUM AND DIFFERENCE FORMULAS Page Theorem cos(αβ cos α cos β -sin α cos(α-β cos α cos β sin α NOTE: cos(αβ cos α cos β cos(α-β cos α -cos β Proof of cos(α-β cos α cos β sin α Let s use a unit circle

Διαβάστε περισσότερα

MECHANICAL PROPERTIES OF MATERIALS

MECHANICAL PROPERTIES OF MATERIALS MECHANICAL PROPERTIES OF MATERIALS! Simple Tension Test! The Stress-Strain Diagram! Stress-Strain Behavior of Ductile and Brittle Materials! Hooke s Law! Strain Energy! Poisson s Ratio! The Shear Stress-Strain

Διαβάστε περισσότερα

DETERMINATION OF FRICTION COEFFICIENT

DETERMINATION OF FRICTION COEFFICIENT EXPERIMENT 5 DETERMINATION OF FRICTION COEFFICIENT Purpose: Determine μ k, the kinetic coefficient of friction and μ s, the static friction coefficient by sliding block down that acts as an inclined plane.

Διαβάστε περισσότερα

Candidate Number. General Certificate of Education Advanced Level Examination June 2010

Candidate Number. General Certificate of Education Advanced Level Examination June 2010 Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials General Certificate of Education Advanced Level Examination June 2010 Question 1 2 Mark Physics

Διαβάστε περισσότερα

CHAPTER 48 APPLICATIONS OF MATRICES AND DETERMINANTS

CHAPTER 48 APPLICATIONS OF MATRICES AND DETERMINANTS CHAPTER 48 APPLICATIONS OF MATRICES AND DETERMINANTS EXERCISE 01 Page 545 1. Use matrices to solve: 3x + 4y x + 5y + 7 3x + 4y x + 5y 7 Hence, 3 4 x 0 5 y 7 The inverse of 3 4 5 is: 1 5 4 1 5 4 15 8 3

Διαβάστε περισσότερα

Homework 8 Model Solution Section

Homework 8 Model Solution Section MATH 004 Homework Solution Homework 8 Model Solution Section 14.5 14.6. 14.5. Use the Chain Rule to find dz where z cosx + 4y), x 5t 4, y 1 t. dz dx + dy y sinx + 4y)0t + 4) sinx + 4y) 1t ) 0t + 4t ) sinx

Διαβάστε περισσότερα

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 19/5/2007

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 19/5/2007 Οδηγίες: Να απαντηθούν όλες οι ερωτήσεις. Αν κάπου κάνετε κάποιες υποθέσεις να αναφερθούν στη σχετική ερώτηση. Όλα τα αρχεία που αναφέρονται στα προβλήματα βρίσκονται στον ίδιο φάκελο με το εκτελέσιμο

Διαβάστε περισσότερα

DESIGN OF MACHINERY SOLUTION MANUAL h in h 4 0.

DESIGN OF MACHINERY SOLUTION MANUAL h in h 4 0. DESIGN OF MACHINERY SOLUTION MANUAL -7-1! PROBLEM -7 Statement: Design a double-dwell cam to move a follower from to 25 6, dwell for 12, fall 25 and dwell for the remader The total cycle must take 4 sec

Διαβάστε περισσότερα

Section 8.3 Trigonometric Equations

Section 8.3 Trigonometric Equations 99 Section 8. Trigonometric Equations Objective 1: Solve Equations Involving One Trigonometric Function. In this section and the next, we will exple how to solving equations involving trigonometric functions.

Διαβάστε περισσότερα

CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education PHYSICS 0625/03

CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education PHYSICS 0625/03 www.xtremepapers.com Centre Number Candidate Number Name CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education PHYSICS 0625/03 Paper 3 Candidates answer on the Question

Διαβάστε περισσότερα

EE512: Error Control Coding

EE512: Error Control Coding EE512: Error Control Coding Solution for Assignment on Finite Fields February 16, 2007 1. (a) Addition and Multiplication tables for GF (5) and GF (7) are shown in Tables 1 and 2. + 0 1 2 3 4 0 0 1 2 3

Διαβάστε περισσότερα

CHAPTER 12: PERIMETER, AREA, CIRCUMFERENCE, AND 12.1 INTRODUCTION TO GEOMETRIC 12.2 PERIMETER: SQUARES, RECTANGLES,

CHAPTER 12: PERIMETER, AREA, CIRCUMFERENCE, AND 12.1 INTRODUCTION TO GEOMETRIC 12.2 PERIMETER: SQUARES, RECTANGLES, CHAPTER : PERIMETER, AREA, CIRCUMFERENCE, AND SIGNED FRACTIONS. INTRODUCTION TO GEOMETRIC MEASUREMENTS p. -3. PERIMETER: SQUARES, RECTANGLES, TRIANGLES p. 4-5.3 AREA: SQUARES, RECTANGLES, TRIANGLES p.

Διαβάστε περισσότερα

Forced Pendulum Numerical approach

Forced Pendulum Numerical approach Numerical approach UiO April 8, 2014 Physical problem and equation We have a pendulum of length l, with mass m. The pendulum is subject to gravitation as well as both a forcing and linear resistance force.

Διαβάστε περισσότερα

Inverse trigonometric functions & General Solution of Trigonometric Equations. ------------------ ----------------------------- -----------------

Inverse trigonometric functions & General Solution of Trigonometric Equations. ------------------ ----------------------------- ----------------- Inverse trigonometric functions & General Solution of Trigonometric Equations. 1. Sin ( ) = a) b) c) d) Ans b. Solution : Method 1. Ans a: 17 > 1 a) is rejected. w.k.t Sin ( sin ) = d is rejected. If sin

Διαβάστε περισσότερα

Areas and Lengths in Polar Coordinates

Areas and Lengths in Polar Coordinates Kiryl Tsishchanka Areas and Lengths in Polar Coordinates In this section we develop the formula for the area of a region whose boundary is given by a polar equation. We need to use the formula for the

Διαβάστε περισσότερα

Μονοβάθμια Συστήματα: Εξίσωση Κίνησης, Διατύπωση του Προβλήματος και Μέθοδοι Επίλυσης. Απόστολος Σ. Παπαγεωργίου

Μονοβάθμια Συστήματα: Εξίσωση Κίνησης, Διατύπωση του Προβλήματος και Μέθοδοι Επίλυσης. Απόστολος Σ. Παπαγεωργίου Μονοβάθμια Συστήματα: Εξίσωση Κίνησης, Διατύπωση του Προβλήματος και Μέθοδοι Επίλυσης VISCOUSLY DAMPED 1-DOF SYSTEM Μονοβάθμια Συστήματα με Ιξώδη Απόσβεση Equation of Motion (Εξίσωση Κίνησης): Complete

Διαβάστε περισσότερα

( ) 2 and compare to M.

( ) 2 and compare to M. Problems and Solutions for Section 4.2 4.9 through 4.33) 4.9 Calculate the square root of the matrix 3!0 M!0 8 Hint: Let M / 2 a!b ; calculate M / 2!b c ) 2 and compare to M. Solution: Given: 3!0 M!0 8

Διαβάστε περισσότερα

PHYA1. General Certificate of Education Advanced Subsidiary Examination June 2012. Particles, Quantum Phenomena and Electricity

PHYA1. General Certificate of Education Advanced Subsidiary Examination June 2012. Particles, Quantum Phenomena and Electricity Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials Physics A Unit 1 For this paper you must have: l a pencil and a ruler l a calculator l a Data

Διαβάστε περισσότερα

2 Composition. Invertible Mappings

2 Composition. Invertible Mappings Arkansas Tech University MATH 4033: Elementary Modern Algebra Dr. Marcel B. Finan Composition. Invertible Mappings In this section we discuss two procedures for creating new mappings from old ones, namely,

Διαβάστε περισσότερα

ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ Ανώτατο Εκπαιδευτικό Ίδρυμα Πειραιά Τεχνολογικού Τομέα. Ξενόγλωσση Τεχνική Ορολογία

ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ Ανώτατο Εκπαιδευτικό Ίδρυμα Πειραιά Τεχνολογικού Τομέα. Ξενόγλωσση Τεχνική Ορολογία ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ Ανώτατο Εκπαιδευτικό Ίδρυμα Πειραιά Τεχνολογικού Τομέα Ξενόγλωσση Τεχνική Ορολογία Ενότητα: Principles of an Internal Combustion Engine Παναγιώτης Τσατσαρός Τμήμα Μηχανολόγων Μηχανικών

Διαβάστε περισσότερα

b. Use the parametrization from (a) to compute the area of S a as S a ds. Be sure to substitute for ds!

b. Use the parametrization from (a) to compute the area of S a as S a ds. Be sure to substitute for ds! MTH U341 urface Integrals, tokes theorem, the divergence theorem To be turned in Wed., Dec. 1. 1. Let be the sphere of radius a, x 2 + y 2 + z 2 a 2. a. Use spherical coordinates (with ρ a) to parametrize.

Διαβάστε περισσότερα

5.4 The Poisson Distribution.

5.4 The Poisson Distribution. The worst thing you can do about a situation is nothing. Sr. O Shea Jackson 5.4 The Poisson Distribution. Description of the Poisson Distribution Discrete probability distribution. The random variable

Διαβάστε περισσότερα

Written Examination. Antennas and Propagation (AA ) April 26, 2017.

Written Examination. Antennas and Propagation (AA ) April 26, 2017. Written Examination Antennas and Propagation (AA. 6-7) April 6, 7. Problem ( points) Let us consider a wire antenna as in Fig. characterized by a z-oriented linear filamentary current I(z) = I cos(kz)ẑ

Διαβάστε περισσότερα

10/3/ revolution = 360 = 2 π radians = = x. 2π = x = 360 = : Measures of Angles and Rotations

10/3/ revolution = 360 = 2 π radians = = x. 2π = x = 360 = : Measures of Angles and Rotations //.: Measures of Angles and Rotations I. Vocabulary A A. Angle the union of two rays with a common endpoint B. BA and BC C. B is the vertex. B C D. You can think of BA as the rotation of (clockwise) with

Διαβάστε περισσότερα

Second Order RLC Filters

Second Order RLC Filters ECEN 60 Circuits/Electronics Spring 007-0-07 P. Mathys Second Order RLC Filters RLC Lowpass Filter A passive RLC lowpass filter (LPF) circuit is shown in the following schematic. R L C v O (t) Using phasor

Διαβάστε περισσότερα

Approximation of distance between locations on earth given by latitude and longitude

Approximation of distance between locations on earth given by latitude and longitude Approximation of distance between locations on earth given by latitude and longitude Jan Behrens 2012-12-31 In this paper we shall provide a method to approximate distances between two points on earth

Διαβάστε περισσότερα

Areas and Lengths in Polar Coordinates

Areas and Lengths in Polar Coordinates Kiryl Tsishchanka Areas and Lengths in Polar Coordinates In this section we develop the formula for the area of a region whose boundary is given by a polar equation. We need to use the formula for the

Διαβάστε περισσότερα

WAVE REVIEW. 1. The two graphs show the variation with time of the individual displacements of two waves as they pass through the same point.

WAVE REVIEW. 1. The two graphs show the variation with time of the individual displacements of two waves as they pass through the same point. WAVE REVIEW 1. The two graphs show the variation with time of the individual displacements of two waves as they pass through the same point. displacement A 1 x 1 T time A 1 displacement A 2 x A 2 2 T time

Διαβάστε περισσότερα

1 String with massive end-points

1 String with massive end-points 1 String with massive end-points Πρόβλημα 5.11:Θεωρείστε μια χορδή μήκους, τάσης T, με δύο σημειακά σωματίδια στα άκρα της, το ένα μάζας m, και το άλλο μάζας m. α) Μελετώντας την κίνηση των άκρων βρείτε

Διαβάστε περισσότερα

4.6 Autoregressive Moving Average Model ARMA(1,1)

4.6 Autoregressive Moving Average Model ARMA(1,1) 84 CHAPTER 4. STATIONARY TS MODELS 4.6 Autoregressive Moving Average Model ARMA(,) This section is an introduction to a wide class of models ARMA(p,q) which we will consider in more detail later in this

Διαβάστε περισσότερα

Section 7.6 Double and Half Angle Formulas

Section 7.6 Double and Half Angle Formulas 09 Section 7. Double and Half Angle Fmulas To derive the double-angles fmulas, we will use the sum of two angles fmulas that we developed in the last section. We will let α θ and β θ: cos(θ) cos(θ + θ)

Διαβάστε περισσότερα

Tuesday 24 January 2012 Afternoon

Tuesday 24 January 2012 Afternoon Tuesday 24 January 2012 Afternoon A2 GCE PHYSICS A G484 The Newtonian World *G411590112* Candidates answer on the Question Paper. OCR supplied materials: Data, Formulae and Relationships Booklet (sent

Διαβάστε περισσότερα

derivation of the Laplacian from rectangular to spherical coordinates

derivation of the Laplacian from rectangular to spherical coordinates derivation of the Laplacian from rectangular to spherical coordinates swapnizzle 03-03- :5:43 We begin by recognizing the familiar conversion from rectangular to spherical coordinates (note that φ is used

Διαβάστε περισσότερα

Matrices and Determinants

Matrices and Determinants Matrices and Determinants SUBJECTIVE PROBLEMS: Q 1. For what value of k do the following system of equations possess a non-trivial (i.e., not all zero) solution over the set of rationals Q? x + ky + 3z

Διαβάστε περισσότερα

10.7 Performance of Second-Order System (Unit Step Response)

10.7 Performance of Second-Order System (Unit Step Response) Lecture Notes on Control Systems/D. Ghose/0 57 0.7 Performance of Second-Order System (Unit Step Response) Consider the second order system a ÿ + a ẏ + a 0 y = b 0 r So, Y (s) R(s) = b 0 a s + a s + a

Διαβάστε περισσότερα

Paper Reference. Paper Reference(s) 6665/01 Edexcel GCE Core Mathematics C3 Advanced. Thursday 11 June 2009 Morning Time: 1 hour 30 minutes

Paper Reference. Paper Reference(s) 6665/01 Edexcel GCE Core Mathematics C3 Advanced. Thursday 11 June 2009 Morning Time: 1 hour 30 minutes Centre No. Candidate No. Paper Reference(s) 6665/01 Edexcel GCE Core Mathematics C3 Advanced Thursday 11 June 2009 Morning Time: 1 hour 30 minutes Materials required for examination Mathematical Formulae

Διαβάστε περισσότερα

Practice Exam 2. Conceptual Questions. 1. State a Basic identity and then verify it. (a) Identity: Solution: One identity is csc(θ) = 1

Practice Exam 2. Conceptual Questions. 1. State a Basic identity and then verify it. (a) Identity: Solution: One identity is csc(θ) = 1 Conceptual Questions. State a Basic identity and then verify it. a) Identity: Solution: One identity is cscθ) = sinθ) Practice Exam b) Verification: Solution: Given the point of intersection x, y) of the

Διαβάστε περισσότερα

PARTIAL NOTES for 6.1 Trigonometric Identities

PARTIAL NOTES for 6.1 Trigonometric Identities PARTIAL NOTES for 6.1 Trigonometric Identities tanθ = sinθ cosθ cotθ = cosθ sinθ BASIC IDENTITIES cscθ = 1 sinθ secθ = 1 cosθ cotθ = 1 tanθ PYTHAGOREAN IDENTITIES sin θ + cos θ =1 tan θ +1= sec θ 1 + cot

Διαβάστε περισσότερα

UDZ Swirl diffuser. Product facts. Quick-selection. Swirl diffuser UDZ. Product code example:

UDZ Swirl diffuser. Product facts. Quick-selection. Swirl diffuser UDZ. Product code example: UDZ Swirl diffuser Swirl diffuser UDZ, which is intended for installation in a ventilation duct, can be used in premises with a large volume, for example factory premises, storage areas, superstores, halls,

Διαβάστε περισσότερα

Advanced Subsidiary Unit 1: Understanding and Written Response

Advanced Subsidiary Unit 1: Understanding and Written Response Write your name here Surname Other names Edexcel GE entre Number andidate Number Greek dvanced Subsidiary Unit 1: Understanding and Written Response Thursday 16 May 2013 Morning Time: 2 hours 45 minutes

Διαβάστε περισσότερα

Chapter 7 Transformations of Stress and Strain

Chapter 7 Transformations of Stress and Strain Chapter 7 Transformations of Stress and Strain INTRODUCTION Transformation of Plane Stress Mohr s Circle for Plane Stress Application of Mohr s Circle to 3D Analsis 90 60 60 0 0 50 90 Introduction 7-1

Διαβάστε περισσότερα

Instruction Execution Times

Instruction Execution Times 1 C Execution Times InThisAppendix... Introduction DL330 Execution Times DL330P Execution Times DL340 Execution Times C-2 Execution Times Introduction Data Registers This appendix contains several tables

Διαβάστε περισσότερα

TMA4115 Matematikk 3

TMA4115 Matematikk 3 TMA4115 Matematikk 3 Andrew Stacey Norges Teknisk-Naturvitenskapelige Universitet Trondheim Spring 2010 Lecture 12: Mathematics Marvellous Matrices Andrew Stacey Norges Teknisk-Naturvitenskapelige Universitet

Διαβάστε περισσότερα

DERIVATION OF MILES EQUATION FOR AN APPLIED FORCE Revision C

DERIVATION OF MILES EQUATION FOR AN APPLIED FORCE Revision C DERIVATION OF MILES EQUATION FOR AN APPLIED FORCE Revision C By Tom Irvine Email: tomirvine@aol.com August 6, 8 Introduction The obective is to derive a Miles equation which gives the overall response

Διαβάστε περισσότερα

PHYA1 (JUN13PHYA101) General Certificate of Education Advanced Subsidiary Examination June 2013. Particles, Quantum Phenomena and Electricity TOTAL

PHYA1 (JUN13PHYA101) General Certificate of Education Advanced Subsidiary Examination June 2013. Particles, Quantum Phenomena and Electricity TOTAL Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials Physics A Unit 1 For this paper you must have: l a pencil and a ruler l a calculator l a Data

Διαβάστε περισσότερα

PHYSICS (SPECIFICATION A) PA10

PHYSICS (SPECIFICATION A) PA10 Surname Centre Number Other Names Candidate Number Leave blank Candidate Signature General Certificate of Education June 2005 Advanced Level Examination PHYSICS (SPECIFICATION A) Unit 10 The Synoptic Unit

Διαβάστε περισσότερα

CHAPTER 101 FOURIER SERIES FOR PERIODIC FUNCTIONS OF PERIOD

CHAPTER 101 FOURIER SERIES FOR PERIODIC FUNCTIONS OF PERIOD CHAPTER FOURIER SERIES FOR PERIODIC FUNCTIONS OF PERIOD EXERCISE 36 Page 66. Determine the Fourier series for the periodic function: f(x), when x +, when x which is periodic outside this rge of period.

Διαβάστε περισσότερα

Surface Mount Multilayer Chip Capacitors for Commodity Solutions

Surface Mount Multilayer Chip Capacitors for Commodity Solutions Surface Mount Multilayer Chip Capacitors for Commodity Solutions Below tables are test procedures and requirements unless specified in detail datasheet. 1) Visual and mechanical 2) Capacitance 3) Q/DF

Διαβάστε περισσότερα

Assalamu `alaikum wr. wb.

Assalamu `alaikum wr. wb. LUMP SUM Assalamu `alaikum wr. wb. LUMP SUM Wassalamu alaikum wr. wb. Assalamu `alaikum wr. wb. LUMP SUM Wassalamu alaikum wr. wb. LUMP SUM Lump sum lump sum lump sum. lump sum fixed price lump sum lump

Διαβάστε περισσότερα

9.09. # 1. Area inside the oval limaçon r = cos θ. To graph, start with θ = 0 so r = 6. Compute dr

9.09. # 1. Area inside the oval limaçon r = cos θ. To graph, start with θ = 0 so r = 6. Compute dr 9.9 #. Area inside the oval limaçon r = + cos. To graph, start with = so r =. Compute d = sin. Interesting points are where d vanishes, or at =,,, etc. For these values of we compute r:,,, and the values

Διαβάστε περισσότερα

Solutions to Exercise Sheet 5

Solutions to Exercise Sheet 5 Solutions to Eercise Sheet 5 jacques@ucsd.edu. Let X and Y be random variables with joint pdf f(, y) = 3y( + y) where and y. Determine each of the following probabilities. Solutions. a. P (X ). b. P (X

Διαβάστε περισσότερα

TSOKOS CHAPTER 6 TEST REVIEW

TSOKOS CHAPTER 6 TEST REVIEW PHYSICS I HONORS/PRE-IB PHYSICS Name: DEVIL PHYSICS Period: Date: # Marks: XX Raw Score: IB Curve: BADDEST CLASS ON CAMPUS TSOKOS CHAPTER 6 TEST REVIEW S1. Thermal energy is transferred through the glass

Διαβάστε περισσότερα

Modbus basic setup notes for IO-Link AL1xxx Master Block

Modbus basic setup notes for IO-Link AL1xxx Master Block n Modbus has four tables/registers where data is stored along with their associated addresses. We will be using the holding registers from address 40001 to 49999 that are R/W 16 bit/word. Two tables that

Διαβάστε περισσότερα

2821 Friday 9 JUNE 2006 Morning 1 hour

2821 Friday 9 JUNE 2006 Morning 1 hour OXFORD CAMBRIDGE AND RSA EXAMINATIONS Advanced Subsidiary GCE PHYSICS A Forces and Motion 2821 Friday 9 JUNE 2006 Morning 1 hour Candidates answer on the question paper. Additional materials: Electronic

Διαβάστε περισσότερα

Econ 2110: Fall 2008 Suggested Solutions to Problem Set 8 questions or comments to Dan Fetter 1

Econ 2110: Fall 2008 Suggested Solutions to Problem Set 8  questions or comments to Dan Fetter 1 Eon : Fall 8 Suggested Solutions to Problem Set 8 Email questions or omments to Dan Fetter Problem. Let X be a salar with density f(x, θ) (θx + θ) [ x ] with θ. (a) Find the most powerful level α test

Διαβάστε περισσότερα

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 6/5/2006

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 6/5/2006 Οδηγίες: Να απαντηθούν όλες οι ερωτήσεις. Ολοι οι αριθμοί που αναφέρονται σε όλα τα ερωτήματα είναι μικρότεροι το 1000 εκτός αν ορίζεται διαφορετικά στη διατύπωση του προβλήματος. Διάρκεια: 3,5 ώρες Καλή

Διαβάστε περισσότερα

Questions on Particle Physics

Questions on Particle Physics Questions on Particle Physics 1. The following strong interaction has been observed. K + p n + X The K is a strange meson of quark composition u s. The u quark has a charge of +2/3. The d quark has a charge

Διαβάστε περισσότερα

PHYA1 (JAN13PHYA101) General Certificate of Education Advanced Subsidiary Examination January Particles, Quantum Phenomena and Electricity TOTAL

PHYA1 (JAN13PHYA101) General Certificate of Education Advanced Subsidiary Examination January Particles, Quantum Phenomena and Electricity TOTAL Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials Physics A Unit 1 For this paper you must have: l a pencil and a ruler l a calculator l a Data

Διαβάστε περισσότερα

Wednesday 11 June 2014 Afternoon

Wednesday 11 June 2014 Afternoon Wednesday 11 June 2014 Afternoon A2 GCE PHYSICS A G484/01 The Newtonian World *3270355010* Candidates answer on the Question Paper. OCR supplied materials: Data, Formulae and Relationships Booklet (sent

Διαβάστε περισσότερα

Dr. D. Dinev, Department of Structural Mechanics, UACEG

Dr. D. Dinev, Department of Structural Mechanics, UACEG Lecture 4 Material behavior: Constitutive equations Field of the game Print version Lecture on Theory of lasticity and Plasticity of Dr. D. Dinev, Department of Structural Mechanics, UACG 4.1 Contents

Διαβάστε περισσότερα

Μέτρηση Δυναμικών Χαρακτηριστικών Μόνωση Ταλαντώσεων Μετρητές Ταλαντώσεων. Απόστολος Σ. Παπαγεωργίου

Μέτρηση Δυναμικών Χαρακτηριστικών Μόνωση Ταλαντώσεων Μετρητές Ταλαντώσεων. Απόστολος Σ. Παπαγεωργίου Μέτρηση Δυναμικών Χαρακτηριστικών Μόνωση Ταλαντώσεων Μετρητές Ταλαντώσεων Μέτρηση Δυναμικών Χαρακτηριστικών MEASUREMENT OF DAMPING Mass and stiffness of a dynamic system can be determined by its physical

Διαβάστε περισσότερα

ANSWERSHEET (TOPIC = DIFFERENTIAL CALCULUS) COLLECTION #2. h 0 h h 0 h h 0 ( ) g k = g 0 + g 1 + g g 2009 =?

ANSWERSHEET (TOPIC = DIFFERENTIAL CALCULUS) COLLECTION #2. h 0 h h 0 h h 0 ( ) g k = g 0 + g 1 + g g 2009 =? Teko Classes IITJEE/AIEEE Maths by SUHAAG SIR, Bhopal, Ph (0755) 3 00 000 www.tekoclasses.com ANSWERSHEET (TOPIC DIFFERENTIAL CALCULUS) COLLECTION # Question Type A.Single Correct Type Q. (A) Sol least

Διαβάστε περισσότερα

Enthalpy data for the reacting species are given in the table below. The activation energy decreases when the temperature is increased.

Enthalpy data for the reacting species are given in the table below. The activation energy decreases when the temperature is increased. Q1.This question is about the reaction given below. O(g) + H 2O(g) O 2(g) + H 2(g) Enthalpy data for the reacting species are given in the table below. Substance O(g) H 2O(g) O 2(g) H 2(g) ΔH / kj mol

Διαβάστε περισσότερα

Αναερόβια Φυσική Κατάσταση

Αναερόβια Φυσική Κατάσταση Αναερόβια Φυσική Κατάσταση Γιάννης Κουτεντάκης, BSc, MA. PhD Αναπληρωτής Καθηγητής ΤΕΦΑΑ, Πανεπιστήµιο Θεσσαλίας Περιεχόµενο Μαθήµατος Ορισµός της αναερόβιας φυσικής κατάστασης Σχέσης µε µηχανισµούς παραγωγής

Διαβάστε περισσότερα

department listing department name αχχουντσ ϕανε βαλικτ δδσϕηασδδη σδηφγ ασκϕηλκ τεχηνιχαλ αλαν ϕουν διξ τεχηνιχαλ ϕοην µαριανι

department listing department name αχχουντσ ϕανε βαλικτ δδσϕηασδδη σδηφγ ασκϕηλκ τεχηνιχαλ αλαν ϕουν διξ τεχηνιχαλ ϕοην µαριανι She selects the option. Jenny starts with the al listing. This has employees listed within She drills down through the employee. The inferred ER sttricture relates this to the redcords in the databasee

Διαβάστε περισσότερα

Lifting Entry (continued)

Lifting Entry (continued) ifting Entry (continued) Basic planar dynamics of motion, again Yet another equilibrium glide Hypersonic phugoid motion Planar state equations MARYAN 1 01 avid. Akin - All rights reserved http://spacecraft.ssl.umd.edu

Διαβάστε περισσότερα

Jesse Maassen and Mark Lundstrom Purdue University November 25, 2013

Jesse Maassen and Mark Lundstrom Purdue University November 25, 2013 Notes on Average Scattering imes and Hall Factors Jesse Maassen and Mar Lundstrom Purdue University November 5, 13 I. Introduction 1 II. Solution of the BE 1 III. Exercises: Woring out average scattering

Διαβάστε περισσότερα

Code Breaker. TEACHER s NOTES

Code Breaker. TEACHER s NOTES TEACHER s NOTES Time: 50 minutes Learning Outcomes: To relate the genetic code to the assembly of proteins To summarize factors that lead to different types of mutations To distinguish among positive,

Διαβάστε περισσότερα

Second Order Partial Differential Equations

Second Order Partial Differential Equations Chapter 7 Second Order Partial Differential Equations 7.1 Introduction A second order linear PDE in two independent variables (x, y Ω can be written as A(x, y u x + B(x, y u xy + C(x, y u u u + D(x, y

Διαβάστε περισσότερα

ΕΙΣΑΓΩΓΗ ΣΤΗ ΣΤΑΤΙΣΤΙΚΗ ΑΝΑΛΥΣΗ

ΕΙΣΑΓΩΓΗ ΣΤΗ ΣΤΑΤΙΣΤΙΚΗ ΑΝΑΛΥΣΗ ΕΙΣΑΓΩΓΗ ΣΤΗ ΣΤΑΤΙΣΤΙΚΗ ΑΝΑΛΥΣΗ ΕΛΕΝΑ ΦΛΟΚΑ Επίκουρος Καθηγήτρια Τµήµα Φυσικής, Τοµέας Φυσικής Περιβάλλοντος- Μετεωρολογίας ΓΕΝΙΚΟΙ ΟΡΙΣΜΟΙ Πληθυσµός Σύνολο ατόµων ή αντικειµένων στα οποία αναφέρονται

Διαβάστε περισσότερα

Problem Set 9 Solutions. θ + 1. θ 2 + cotθ ( ) sinθ e iφ is an eigenfunction of the ˆ L 2 operator. / θ 2. φ 2. sin 2 θ φ 2. ( ) = e iφ. = e iφ cosθ.

Problem Set 9 Solutions. θ + 1. θ 2 + cotθ ( ) sinθ e iφ is an eigenfunction of the ˆ L 2 operator. / θ 2. φ 2. sin 2 θ φ 2. ( ) = e iφ. = e iφ cosθ. Chemistry 362 Dr Jean M Standard Problem Set 9 Solutions The ˆ L 2 operator is defined as Verify that the angular wavefunction Y θ,φ) Also verify that the eigenvalue is given by 2! 2 & L ˆ 2! 2 2 θ 2 +

Διαβάστε περισσότερα

UNIVERSITY OF CALIFORNIA. EECS 150 Fall ) You are implementing an 4:1 Multiplexer that has the following specifications:

UNIVERSITY OF CALIFORNIA. EECS 150 Fall ) You are implementing an 4:1 Multiplexer that has the following specifications: UNIVERSITY OF CALIFORNIA Department of Electrical Engineering and Computer Sciences EECS 150 Fall 2001 Prof. Subramanian Midterm II 1) You are implementing an 4:1 Multiplexer that has the following specifications:

Διαβάστε περισσότερα

PHYA1 (JAN12PHYA101) General Certificate of Education Advanced Subsidiary Examination January 2012. Particles, Quantum Phenomena and Electricity TOTAL

PHYA1 (JAN12PHYA101) General Certificate of Education Advanced Subsidiary Examination January 2012. Particles, Quantum Phenomena and Electricity TOTAL Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials Physics A Unit 1 For this paper you must have: l a pencil and a ruler l a calculator l a Data

Διαβάστε περισσότερα

Pg The perimeter is P = 3x The area of a triangle is. where b is the base, h is the height. In our case b = x, then the area is

Pg The perimeter is P = 3x The area of a triangle is. where b is the base, h is the height. In our case b = x, then the area is Pg. 9. The perimeter is P = The area of a triangle is A = bh where b is the base, h is the height 0 h= btan 60 = b = b In our case b =, then the area is A = = 0. By Pythagorean theorem a + a = d a a =

Διαβάστε περισσότερα

physicsandmathstutor.com Paper Reference Core Mathematics C4 Advanced Level Tuesday 23 January 2007 Afternoon Time: 1 hour 30 minutes

physicsandmathstutor.com Paper Reference Core Mathematics C4 Advanced Level Tuesday 23 January 2007 Afternoon Time: 1 hour 30 minutes Centre No. Candidate No. Paper Reference(s) 6666/01 Edexcel GCE Core Mathematics C4 Advanced Level Tuesday 23 January 2007 Afternoon Time: 1 hour 30 minutes Materials required for examination Mathematical

Διαβάστε περισσότερα

D Alembert s Solution to the Wave Equation

D Alembert s Solution to the Wave Equation D Alembert s Solution to the Wave Equation MATH 467 Partial Differential Equations J. Robert Buchanan Department of Mathematics Fall 2018 Objectives In this lesson we will learn: a change of variable technique

Διαβάστε περισσότερα